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This manuscript investigates the bias introduced by scaling aftershock ground motions when evaluating the performance of structures subjected to earthquake sequences. The study focuses on different hysteretic behaviors exhibited by structures and selects eight intensity measures as scale indicators. A benchmark database comprising 274 recorded mainshock–aftershock ground motions is utilized for analysis. The findings reveal that scaling aftershock records using intensity measures such as SI (seismic intensity), PGV (peak ground velocity), IC (Arias intensity), and Sa (spectral acceleration) relative to mainshock records effectively controls the mean bias within 30% throughout the entire period range, given a maximum scale factor of 10.0. However, it is observed that the additional damage in systems exhibiting un-degrading hysteretic behavior is more significantly affected by aftershock ground motion scaling compared to systems with degrading hysteretic behavior. Furthermore, scaling aftershock ground motions upwards using relative Sa tends to overestimate the additional damage incurred by structures. These results emphasize the importance of considering the specific hysteretic behavior of structures when applying aftershock ground motion scaling, as well as selecting appropriate intensity measures for accurate evaluation of structural performance. [ABSTRACT FROM AUTHOR]

This manuscript investigates the bias introduced by scaling aftershock ground motions when evaluating the performance of structures subjected to earthquake sequences. The study focuses on different hysteretic behaviors exhibited by structures and selects eight intensity measures as scale indicators. A benchmark database comprising 274 recorded mainshock–aftershock ground motions is utilized for analysis. The findings reveal that scaling aftershock records using intensity measures such as SI (seismic intensity), PGV (peak ground velocity), IC (Arias intensity), and Sa (spectral acceleration) relative to mainshock records effectively controls the mean bias within 30% throughout the entire period range, given a maximum scale factor of 10.0. However, it is observed that the additional damage in systems exhibiting un-degrading hysteretic behavior is more significantly affected by aftershock ground motion scaling compared to systems with degrading hysteretic behavior. Furthermore, scaling aftershock ground motions upwards using relative Sa tends to overestimate the additional damage incurred by structures. These results emphasize the importance of considering the specific hysteretic behavior of structures when applying aftershock ground motion scaling, as well as selecting appropriate intensity measures for accurate evaluation of structural performance.

The mainshock (MS) is often accompanied by a number of aftershocks (AS). The existence of AS may cause the seismic demand to be greater than the MS. In order to better evaluate the impact of AS, this paper takes RC columns as the research object and performs incremental dynamic analysis (IDA) on the actual recorded mainshock-aftershocks (MS-AS). The Park–Ang model and incremental damage index are used to quantify the effect of the MS and AS, respectively. The damage and fragility analysis of the parameters such as reinforcement ratio, axial compression ratio and shear-span ratio are carried out respectively. The results show that the seismic demand of the MS-AS is greater than the MS. Besides, the damage of the column gradually increases with the increase of axial compression ratio and shear-span ratio, and gradually decreases with the increase of the reinforcement ratio. When the seismic design grade is 7, 8, and 9 degree, the maximum increase rate of additional damage caused by aftershocks is 7, 13, and 15% of the MS, respectively. When the column is in a medium damaged and a severely damaged state, the growth rate of additional damage can be estimated to be 12.7 and 11% of the MS, respectively. The fragility of columns in different damage states under the action of MS-AS is greater than that of MS. Reducing the axial pressure ratio can greatly reduce the damage probability of columns in different damage states. The effect of the MS-AS can be comprehensively considered to select appropriate design parameters in the design, and the additional damage caused by the AS can be estimated according to the damage condition of the column. [ABSTRACT FROM AUTHOR]

The mainshock (MS) is often accompanied by a number of aftershocks (AS). The existence of AS may cause the seismic demand to be greater than the MS. In order to better evaluate the impact of AS, this paper takes RC columns as the research object and performs incremental dynamic analysis (IDA) on the actual recorded mainshock-aftershocks (MS-AS). The Park–Ang model and incremental damage index are used to quantify the effect of the MS and AS, respectively. The damage and fragility analysis of the parameters such as reinforcement ratio, axial compression ratio and shear-span ratio are carried out respectively. The results show that the seismic demand of the MS-AS is greater than the MS. Besides, the damage of the column gradually increases with the increase of axial compression ratio and shear-span ratio, and gradually decreases with the increase of the reinforcement ratio. When the seismic design grade is 7, 8, and 9 degree, the maximum increase rate of additional damage caused by aftershocks is 7, 13, and 15% of the MS, respectively. When the column is in a medium damaged and a severely damaged state, the growth rate of additional damage can be estimated to be 12.7 and 11% of the MS, respectively. The fragility of columns in different damage states under the action of MS-AS is greater than that of MS. Reducing the axial pressure ratio can greatly reduce the damage probability of columns in different damage states. The effect of the MS-AS can be comprehensively considered to select appropriate design parameters in the design, and the additional damage caused by the AS can be estimated according to the damage condition of the column.

• A multiaxial total life prediction method based on short crack growth is proposed. • The additional damage from non-proportional loading path is characterized. • Effect of shear stress on crack growth under tensile/compressive stress is considered. • The proposed method is verified by two materials under multiaxial loading. A total life prediction method based on short crack propagation considering additional damage from non-proportional loading is proposed under multiaxial fatigue loading. Firstly, a new calculation method of equivalent stress range is proposed to consider the effect of shear stress on crack propagation under tensile or compressive stress, then it is further modified to consider the additional damage. Combined with Paris formula and crack closure correction, a total life prediction method is proposed. The life results were used to verify the proposed method for two materials, which showed that most errors are within a factor of 3. [ABSTRACT FROM AUTHOR]

To investigate the influence of mainshock-aftershock sequences on displacement responses, failure mode, global damage evolution, etc of structures, the sequences are generated by combining the next generation attenuation (NGA) relationship for earthquakes with the relationship between main shock and strong aftershock. The modified section damage ratio model is applied to analyze additional damage of an example structure under strong aftershocks, as well as probabilistic accumulative damage. The investigation indicates that additional damage incurred by strong aftershocks tends to increase as their probabilities of exceedance (POE) decrease. Approximate negative correlation could be observed between the damage ratios of main shocks and those added by strong aftershocks. When structures experience substantial damage under main shocks, probabilistic accumulative damage of structures would change significantly even coupled with damage induced by low-level aftershocks. Additional damage would be aggravated by so-called analogous resonance phenomenon when the predominant periods of the response spectra of these aftershocks are close to the vibration periods of damaged structures under main shocks. [ABSTRACT FROM AUTHOR]